1. Set S contains points whose abscissa and ordinate are both natural numbers. Point P, an element in set S has the property that the sum of the distances from point P to the point (3,0) and the point (0,5) is the lowest among all elements in set S. What is the sum of abscissa and ordinate of point P?

Any point on the line x/3 + y/5 =1 will have the shortest overall distance. However, we need to have integral coordinates. So, we need to find points with integral coordinates as close as possible to the line 5x + 3y =15.

2. Region R is defined as the region in the first quadrant satisfying the condition 3x + 4y < 12. Given that a point P with coordinates (r, s) lies within the region R, what is the probability that r > 2?

Line 3x + 4y =12 cuts the x-axis at (4, 0) and y axis at (0, 3)

The region in the first quadrant satisfying the condition 3x + 4y < 12 forms aright triangle with sides 3, 4 and 5. Area of this triangle = 6 sq units.